Chapter 6 Adequacy of Linear Regression Model: Coefficient of Determination

Description:  This simulation depicts how the sum of the squared differences reduces as the two variables are correlated, and hence giving a lower value for the sum of the squares of the residuals.

Keywords:  regression, linear regression, sum of squared differences, sum of square of residuals, correlation coefficient, coefficient of determination.

Learning Objectives:  After successful completion of running the simulation with proper questions asked by the instructor, the student would be able to 1) note geometrically what the squared differences mean 2) note geometrically what the sum of the squared residuals mean 3) how the two sums are related to the coefficient of determination and correlation coefficient.

Full Resources:  The full resources for the topic of the nonlinear regression models are given here which include textbook content, a PowerPoint presentation, a multiple-choice test, audiovisual lectures, and application examples.

Software Requirements:  Latest versions of Safari,  Microsoft Edge, Firefox, Google Chrome.

Credits:  Design Team: Autar Kaw.  Software development: Mayank Pandey and Autar Kaw.
We acknowledge the immense help of the third party libraries: almond-0.2.9.js, easing-equations-r12,FileSaver-b8054a2.js, fontawesome-webfont-3.0.2.svg, jama-1.0.2, jquery-2.1.0.js, lodash-2.4.1.js, pegjs-0.7.0.js, seedrandom-2.4.2.js, text-2.0.12.js, Tween-r12.js, Phet

Acknowledgments: This material is based upon work supported partially by the National Science Foundation under Grant Number 2013271. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

All Simulations: Here is the link for all the simulations developed.